Pertanyaan

x → ∞ lim ( x 2 + 2 x − 3 − ( x + 1 ) ) = …

$x \to \infty lim (x^{2} + 2 x - 3 - (x + 1)) = \dots$

A. Fatta

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Ingat jika . Perhatikan perhitungan berikut! Jadi, . Oleh karena itu, jawaban yang benar adalah C.

Ingat jika $limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of a x squared plus q x plus r end root close parentheses equals fraction numerator b minus q over denominator 2 square root of a end fraction$ .

Perhatikan perhitungan berikut!

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of x squared plus 2 x minus 3 end root minus open parentheses x plus 1 close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of x squared plus 2 x minus 3 end root minus square root of open parentheses x plus 1 close parentheses squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of x squared plus 2 x minus 3 end root minus square root of x squared plus 2 x plus 1 end root close parentheses end cell row blank equals cell fraction numerator 2 minus 2 over denominator 2 square root of 1 end fraction end cell row blank equals 0 end table$

Jadi, limit as x rightwards arrow infinity of open parentheses square root of x squared plus 2 x minus 3 end root minus open parentheses x plus 1 close parentheses close parentheses equals 0 .

Oleh karena itu, jawaban yang benar adalah C.